Simple Nature - Light and Matter

sity of matter from that. It turns out that we can do this by observingthe cosmic microwave background (CMB) radiation, whichis the light left over from the brightly glowing early universe, whichwas dense and hot. As the universe has expanded, light waves thatwere in flight have expanded their wavelengths along with it. Thisafterglow of the big bang was originally visible light, but after billionsof years of expansion it has shifted into the microwave radiopart of the electromagnetic spectrum. The CMB is not perfectlyuniform, and this turns out to give us a way to measure the universe’scurvature. Since the CMB was emitted when the universewas only about 400,000 years old, any vibrations or disturbances inthe hot hydrogen and helium gas that filled space in that era wouldonly have had time to travel a certain distance, limited by the speedof sound. We therefore expect that no feature in the CMB shouldbe bigger than a certain known size. In a universe with negativespatial curvature, the sum of the interior angles of a triangle is lessthan the Euclidean value of 180 degrees. Therefore if we observea variation in the CMB over some angle, the distance between twopoints on the sky is actually greater than would have been inferredfrom Euclidean geometry. The opposite happens if the curvature ispositive.This observation was done by the 1989-1993 COBE probe, andits 2001-2009 successor, the Wilkinson Microwave Anisotropy Probe.The result is that the angular sizes are almost exactly equal to whatthey should be according to Euclidean geometry. We therefore inferthat the universe is very close to having zero average spatial curvatureon the cosmological scale, and this tells us that its averagedensity must be within about 0.5% of the critical value. The yearssince COBE and WMAP mark the advent of an era in which cosmologyhas gone from being a field of estimates and rough guessesto a high-precision science.If one is inclined to be skeptical about the seemingly precise answersto the mysteries of the cosmos, there are consistency checksthat can be carried out. In the bad old days of low-precision cosmology,estimates of the age of the universe ranged from 10 billionto 20 billion years, and the low end was inconsistent with the ageof the oldest star clusters. This was believed to be a problem eitherfor observational cosmology or for the astrophysical models used toestimate the ages of the clusters: “You can’t be older than yourma.” Current data have shown that the low estimates of the agewere incorrect, so consistency is restored. (The best figure for theage of the universe is currently 13.8 ± 0.1 billion years.)q / The angular scale of fluctuationsin the cosmic microwavebackground can be used to inferthe curvature of the universe.Dark energy and dark matterNot everything works out so smoothly, however. One surpriseisthat the universe’s expansion is not currently slowing down, as hadbeen expected due to the gravitational attraction of all the matterSection 7.4 ⋆ General Relativity 435